In this work, we develop a robust adaptive well-balanced and positivity-preserving central-upwind scheme on unstructured triangular grids for shallow water equations. The numerical method is an extension of the scheme from [{\sc Liu {\em et al.}},J. of Comp. Phys, 374 (2018), pp. 213 - 236]. As a part of the adaptive central-upwind algorithm, we obtain local a posteriori error estimator for the efficient mesh refinement strategy. The accuracy, high-resolution, and efficiency of the new adaptive central-upwind scheme are demonstrated on a number of challenging tests for shallow water models.
We propose a one-dimensional Saint-Venant (open channel) model overland flows including a water input--output source term modelling recharge via rainfall and infiltration (or exfiltration). We derive the model via asymptotic reduction from the two-dimensional Navier--Stokes equations under the shallow water assumption, with boundary conditions including recharge via ground infiltration and runoff. This new model recovers existing models as sepcial cases, and adds more scope by adding a water-mixing friction terms that depends on the rate of water recharge. We prospose a novel entropy function …
Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system
Université Paris 13（巴黎第十三大学）；Inria（法国国家信息与自动化研究所）；CEREMA（中央研究与评估中心）；Sorbonne University（索邦大学）；Université Paris-Est（巴黎东大学）；CNRS（法国国家科学研究中心）；UPEM（巴黎东马恩拉瓦莱大学）；UPEC（巴黎十二大学）
We present a splitting method for the one-dimensional Saint-Venant-Exner equations used for describing the bed evolution in shallow water systems. We adapt the flux vector splitting approach of Toro and Vazquez-Cendòn and identify one subsystem of conservative equations (advection system) and one of non-conservative equations (pressure system), both having a very simple eigenstructure compared to the full system. The final numerical scheme is constructed using a Godunov-type path-conservative scheme for the pressure system and a simple conservative Godunov method for the advection system and s…
This research is aimed at achieving an efficient digital infrastructure for evaluating risks and damages caused by tsunami flooding. It is mainly focused on the suitable modeling of debris dynamics for a simple (but accurate enough) assessment of damages. For different reasons including computational performance and Big Data management issues, we focus our research on Eulerian debris flow modeling. Rather than using complex multiphase debris models, we rather use an empirical transportation and deposition model that takes into account the interaction with the main water flow, friction/contact …
In this paper, we describe a numerical algorithm for the self-consistent simulations of surface water and sediment dynamics. The method is based on the original Lagrangian-Eulerian CSPH-TVD approach for solving the Saint-Venant and Exner equations, taking into account the physical factors essential for the understanding of the shallow water and surface soil layer motions, including complex terrain structure and its evolution due to sediment transport. Additional Exner equation for sediment transport has been used for the numerical CSPH-TVD scheme stability criteria definition. By using OpenMP-…
